Your questions, I think, raise some confusion about the Emerald Buddha's chronology. I will try to answer those first, and then move onto your substantive questions about the Emerald Buddha vis-a-vis the formation of the Thai state, Buddhist legitimacy, and Cambodia.

The Emerald Buddha is a statue of the Gautama Buddha, about 66 cm tall, and probably made of jasper. It has been traditionally dated to the mid 15th century. It currently sits in Wat Phra Kaew (the aptly named "Temple of the Emerald Buddha) on the grounds of the palace in Bangkok.

Its history is first described by European historians in the 1930s, when French colonial scholars translate vernacular Northern Thai palm-leaf manuscripts of "The Chronicle of the Emerald Buddha" into French and then English.

The Chronicle describes first the creation of the Emerald Buddha by Vishnu and Indra, and its subsequent journey to Sri Lanka, Bagan, and (yes) to Angkor. Here the journey is not literal- the boat of the Burmese monks is "blown off course" and they arrive, somewhat implausibly at Angkor, for example. Instead, the story is a metaphor, for the transfer of Theravada Buddhist learning/legitimacy from India to SEA.

The Thai section of the story picks up here. The Angkorian king unjustly drowns one of his subjects, and as a result is punished and killed by a naga- monks afraid for the Emerald Buddha's safety, bring it north. This is another extension of the just-so story elaborated above. The transition in power from the Angkorians to the Ayutthyans was the result of Khmer immorality, and thus (the future nation of) Siam would be a more appropriate home for the Emerald Buddha.

The discovery of the Emerald Buddha comes when it emerges- miraculously- from behind the plaster where it had been hidden in Chaing Rai. This marks the beginning of the movement of power within Thailand which forms an important part of the narrative for the post-Ayutthya Thai state. It is also worth noting here that miraculous-discovery-of-Buddha statue is a well-established trope. Many temples have stories about their statue and its origins. The city of Phnom Penh was ostensibly founded on its location because of the discovery of a Buddha statue floating in a log on the river. So that miracle of the Emerald Buddha does not make it a unique symbol of Buddhist power for that reason per se.

In the next sections of the narrative, the Emerald Buddha is first taken from the Northeast to the Lao kingdom in Luang Prabang, and then to Vientiane. This continues the theme of the theme, but with a twist. The mantle of Buddhist kingship has passed now to within the Tai-speaking (and what the later Thai state would try to define as Thai) world. Not only does this narrative position the Siamese state to be the successor to previous Buddhist kingdoms, but also to Lanna, Lanxang, and other Tai-speaking states. As the "paramount symbol of modern Thailand" as you put it, the Emerald Buddha represents Thai identity and Buddhism in their most expansive sense, under the auspices of the Thai state.

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You might notice that in the previous section, I did not give a great deal of history on the Emerald Buddha as a material object. This is for two reasons. First, I don't know much about its material history- we do not even definitively know what it is made of, for example. Second, the metaphor of the Emerald Buddha is much more interesting than the actual object. To answer your question "if the Emerald Buddha [was so important that it would become] the paramount symbol of modern Thailand, why didn't earlier rulers try to capture it?"- it is because the Emerald Buddha does not hold meaning per se, but rather it was imbued with that meaning over time. It was not the holiest of all Buddha statues and so coveted by all rulers- it was a piece of war booty that came to symbolize the legitimacy of the new Thai nation-state. (This sequential moving of valuable war-booty pieces was not uncommon in SEA during the period either. Another famous example are Angkorian bronze statues which were looted first to Ayutthya, then to Bagan, then to Mandalay.)

I think the Cambodian case you raise here helps to prove this point. One of the most popular Khmer national myths is the story of Preah Ko and Preah Keo (Sacred Cow and Sacred Gem- the Thai Phra Kaew is a direct borrowing from Old Khmer). In the story Preah Ko and Preah Keo are twins who possess miraculous powers, sacred objects, and wisdom/Buddhist texts. In some stories, Preah Ko has sacred treasures in his belly, and must be cut open to release them. In some stories the pair are statues/statues containing treasure, and a metaphor for the wealth of Angkor. In the most common retelling of the story, the pair are captured by the Siamese and taken as hostages, after the Siamese fire coins out of their cannons which the greedy Cambodian soldiers stop to pick up from the ground. By this un-Buddhist act, Cambodia had lost its national palladium.

The Cambodian Wat Preah Keo houses its own Emerald Buddha, as well. It was manufactured out of crystal by French jewelers during the colonial era. This does not make it any less the Emerald Buddha than Thailand's though. For Thailand, its Emerald Buddha symbolizes a national myth of divine Buddhist kingship that ties Thai kings back to the time of the Buddha (and also conveniently lay out the geobody of the early Thai state). For Cambodians, their Emerald Buddha symbolizes a national myth of perseverance and survival through trials and tribulations. Even though Preah Keo was taken, he is still here, etc. (Preah Ko Preah Keo also serves as a just-so story for the transfer of what were perceived to be Khmer cultural markers to Thai society during the Ayutthya period- Khmer style script, Theravada Buddhism, courtly music, dance, etc.)

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I hope that I have dispelled the notion in your titular question that the Emerald Buddha was "significant to Southeast Asian Theravada Buddhism". The stories around the Emerald Buddha come from a shared tradition of tropes present in folklore across Mainland SEA. Its significance came when Siamese kings saw themselves as increasingly "significant to Southeast Asian Theravada Buddhism" and began to afford their objects such significance as well. Thailand's Emerald Buddha is also not unique in this regard, Cambodia's Emerald Buddha offers a counter-claim to Buddhist legitimacy. And both sets of traditions draw on much deeper roots.

It only gets you so far to look at the chain of possession for the object, without thinking about the symbol. To do so would ignore the more interesting questions, like "what power structures does this symbol uphold?" and "who is invested in this symbol?"